He (the author) said, “Ism is identified through: الْخَفْضِ (having a kasra in the last letter), التَّنْوِينِ, addition of لاَمٍ و َأَلِفْ (Alif and Lam), and the حروف (particles) that give khafdh (kasra to the word), and they (the particles) are: من (from), إلى (to), عن (about), على (upon), في (in), Rubba (رب), باء (with), كاف (like), لام (for), and the particles of oath (al-qasm): واو, باء, and تاء.

As for Al-Khafd, it’s an expression of Kasra which occurs due to an ‘Amil (agent such as Min) or that which takes it’s place, such as the Kasra on the Ra in the word Bakr and ‘Amr: مررت ببكر (I passed by Bakr), and هذا كتاب عمرو (This is ‘Amr’s Book). Both ‘Amr and Bakr are Ism because of the Khafd (Kasra) at the end of the two words.

As for Alif and Lam, it indicates that the word is a noun. If alif and lam can be attached to it then it’s an ism, so the word Rajulun (رجل) can accept alif and Lam, and so the word becomes ar-Rajul (الرجل).

As for Huruf al-Khafd (Particles that give Khafd), from the many meanings of Min is that which gives the meaning of beginning, ex. سافرت من القاهرة ‘I traveled from Cairo’. For the meanings of the Huruf, they’re given above.

As for the particles of Khafdh which are particles of Oath, they are Waw, Ba’ and Ta’:

As for واو It only comes before a proper noun, such as والطور, so there is a kasrah on the Ra’, and the meaning is, By the Oath of Tur.
As for باء, it’s not restricted to any word, but it enters on a proper noun including pronouns, such as بك لأضربن الكسول, ‘I swear by you, I will hit the lazy person’. But Bika will be read with a Fatha on the Kaf, not with a Kasra, though it’s implied.
As for تاء, it only enters upon Lafdh al-Jalal (Allah ta’ala). Hafidh ibn Qayyim says, “تالله لقد وجب علينا حبّ أبي بكر”, By Allah ta’ala, it’s wajib on us to love Abu Bakr. The Lafhdul Jalalah (Allah ta’ala) get’s a kasrah.

To recap, all of the four signs tell us that the word after them is a noun, and not a verb or a particle.

There are four nouns (Ism) in the first ayah, why are there four, and which ones are they?
بِسمِ – The first letter is a Harful Khafdh (a particle that gives kasra) and it’s one of the particles that’s listed above, and so there’s a kasrah on Bismi.
ٱلله – Lafdh ul Jalalah, This is an Ism because it has a Kasra (in the context of the Ayah) and it has Alif and Lam in the beginning.
الرَّحْمٰنِ – This is an Ism because it has Alif and Lam in the beginning.
الرَّحِيـمِ – This is an Ism because it has Alif and Lam in the beginning.

Every single word that is used in the Arabic language is a noun, verb or a particle.

اسم is a word that indicates towards a meaning in itself, and isn’t joined with one of the three times (past, present, and future). Examples included Muhammed, رجل (a man), ‘عصا (a stick), etc.

فعل is a verb and it indicates towards a meaning in itself, and is joined with one of the three times (past, present, and future). Examples include, كتب (he wrote), the word indicates towards writing and is joined with the past tense. يكتب (he’s writing), the word indicates towards writing and is joined with the present tense, and اكتب (a command to write), the word indicates towards writing and is joined with the future tense/command.

There are three kinds of verbs: past, present/future and command:
1. ماضي (past tense) indicates towards an act done in the past, such as كتب (he wrote).
2. مضارع (present/future tense) indicates towards an act that is being done in the present time or will occur in the future, such as يفهم (he’s understanding or he will understand).
3. امر (command) is what indicates towards an act that is sought/ordered to be done in the future, example: افهم (understand)

حرف is a word that indicates towards a meaning in other than it (has no specific meaning in itself, requires something else to make it meaningful). Examples: من (from), this word indicates towards a meaning of beginning, and the understanding isn’t completed until it’s linked with another word, such as خرجت من البيت ‘I left the house’. The من indicates that you left the house, which was the start point of your travel.

أبدأُ بالحمدِ مُصَلِّياً على مُحمَّدٍ خَيِر نبيْ أُرســـــِلا
The Arabic language is the noblest of all languages, with many sciences. One of those sciences is النحو or Grammar. Grammar was first codified due to the influx of foreign people in the Islamic world, thus Sayyidina ‘Ali ordered Abul Aswad ad-Du’liyyu to codify the rules of Grammar; it’s recorded that Sayyidina ‘Ali started the grammatical rules, then Abul Aswad finished it. The ruling for learning Nahw is Fard Kifayya, though if one makes constant mistakes in recitation of Quran such that the meaning changes, it becomes wajib on the individual to learn it. The benefit of learning Nahw is that it protects the tongue from making errors, and one can understand The Quran and Noble Ahadith which are the foundations of the Din. Nahw concerns the position or state of the last letter in the Arabic language, which determines the meaning of the word in relation to the sentence.
The posts will be taken from the book التحفه السنيه بشرح المقدمه الاجروميه. And can be downloaded from: http://al-mostafa.info/data/arabic/depot2/gap.php?file=012920.pdf

Bismillah
First sentence of the text:
“Speech or a sentence (الكلام) is composed of compounded words which gives benefit (meaning) when coined”

By اللفظ (word), the author means that which has sound and is composed of letters from the Arabic language, ex. Ahmed, يكتب (he writes), Sa’id, etc.

By المركب (compound), the author means that which is composed of two or more words, such as محمد مسافر Muhammed is a traveler. According to the Grammarians, speech can be composed of only one word, if it has something hidden or implied, such as if someone were to say, “Who’s your brother? The response would be, “Muhammed”, if one were to express the hidden words, it would be, “My brother is Muhammed”.

By المفيد (benefit), he means that the one addressed has received the message and isn’t waiting to receive some other information from the addressee to finish the news. So if one were to say, ‘If the teacher enters’, this would not be speech since the one being addressed is waiting for the news as to what would happen if the teacher enters, to complete the meaning one can say ‘if the teacher enters, the students quite down’.

By الوضع (coined), the author means words coined by the Arabic Alphabet which indicates towards a meaning, such as جاء which in the Arabic language gives the meaning of coming in the past tense, or Muhammed, which is a person whose name is Muhammed.
Examples: محمد مسافر – Muhammed is a Travellor. This fulfills all of the conditions of speech (kalam), since it’s composed of two words, which gives meaning and is coined in the Arabic language. Another example is, يضئ القمر ليلا The Moon shines at night.